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Weak amenability for Fourier algebras of 1-connected nilpotent Lie groups. (English) Zbl 1328.43005
B. E. Forrest and V. Runde [Math. Z. 250, No. 4, 731–744 (2005; Zbl 1080.22002)] conjectured that the Fourier algebras of non-abelian connected Lie groups are not weakly amenable. This was previously known to be true for non-abelian compact groups, the real \(a x + b\) groups and hence, the semisimple Lie groups. In this paper, the authors confirm this conjecture for \(1\)-connected non-abelian nilpotent Lie groups.

43A30 Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.
46J10 Banach algebras of continuous functions, function algebras
47B47 Commutators, derivations, elementary operators, etc.
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